偏微分方程
2009-6
世界图书出版公司
约翰
249
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A considerable amount of new material has been added to this edition.There is an extensive discussion of real analytic functions of several variablesin Chapter 3. This permits estimation of the size of the domain of existencein the Cauchy-Kowalevski theorem. A first application of these estimatesconsists in a rigorous proof of a new version of Holmgren's uniquenesstheorem for linear analytic partial differential equations （only sketched inthe earlier editions）. As another application （following Schauder） we give asecond proof for existence of solutions of the initial value problem forsymmetric hyperbolic systems in Chapter 5. Chapter 6 now includes a moredetailed study of the Hilbert spaces with applications to the boundarybehavior of solutions of the Dirichlet problem in higher dimensions. ToChapter 7 there has been added a proof of Widder's theorem on non-negativesolutions of the heat equation. Finally, a new chapter, Chapter 8, containsH. Lewy's construction of a linear differential equation without solutions.There are also more problems, designed, in part, to extend the materialdiscussed in the text. 1 am particularly indebted to my colleague Percy A. Deift of the CourantInstitute of New York University, to Prof. A. Garder of the Southern IllinoisUniversity at Edwardsville, Illinois, and to Dr. George Dassios of theNational Technical University of Athens, Greece, for taking the trouble tocompile lists of errors in the third edition. I hope that these have all beencorrected and not too many new ones added in the present edition.
本书是一部非常优秀的介绍偏微分方程的入门书籍，可以作为研究生阶段学习的基石。本书详尽地介绍了偏微分方程理论的重要方面，并从数学分析的角度做了进一步的探讨。本书是第4版，增加了全新的一章讲述无解线性方程的Lewy例子。
作者：(德国)约翰(John.F.)
Chapter 1 The Single First-Order Equation 1. Introduction 2. Examples 3. Analytic Solution and Approximation Methods in a Simple Example Problems 4. Quasi-linear Equations 5. The Cauchy Problem for the Quasi-linear Equation 6. Examples Problems 7. The General First-Order Equation for a Function of Two Variables 8. The Cauchy Problem 9. Solutions Generated as Envelopes ProblemsChapter 2 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 1. Characteristics for Linear and Quasi-linear Second-order Equations 2. Propagation of Singularities 3. The Linear Second-Order Equation Problems 4. The One-Dimensional Wave Equation Problems 5. Systems of First-Order Equations 6. A Quasi-linear System and Simple Waves ProblemChapter 3 Characteristic Manifolds and the Cauchy Problem 1. Notation of Laurent Schwartz Problems 2. The Cauchy Problem Problems 3. Real Analytic Functions and the Cauchy-Kowalevski Theorem (a) Multiple infinite series Problems (b) Real analytic functions Problems (c) Analytic and real analytic functions Problems (d) The proof of the Cauchy-Kowalevski theorem Problems 4. The Lagrange-Green Identity 5. The Uniqueness Theorem of Holmgren Problems 6. Distribution Solutions ProblemsChapter 4 The Laplace Equation 1. Green's Identity. Fundamental Solutions, and Poisson's Equation Problems 2. The Maximum Principle Problems 3. The Dirichlet Problem, Green's Function, and Poisson's Formula Problems 4. Proof of Existence of Solutions for the Dirichlet Problem Using Subharmonic Functions ("Perron's Method") Problems 5. Solution of the Dirichlet Problem by Hilbert-Space Methods ProblemsChapter 5 Hyperbolic Equations in Higher Dimensions 1. The Wave Equation in n-Dimensional Space (a) The method of spherical means Problems (b) Hadamard's method of descent Problems ……Chapter 6 Higher-Order Elliptic Equations with ConstantChapter 7 Parabolic EquationsChapter 8 H.Lewy's Example of a Linear EquationBibliographyGlossaryIndex
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《偏微分方程(第4版)(英文版)》是由世界图书出版公司出版的。
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非常好的一本书，数学教师可以多学习学习
买书就上网，打折多海送到家。
不过有点难度，加上英文水平有限，勉强看了一会，希望有时间能完整看完
经典教材，一定要有！
主要讲双曲PDE,作者本人也是大牛
便宜，版本新。
台湾国立的视频教程课本！！！！！
该教材是台湾国立交通大学偏微分方程授课之教材，理论性较强。适合于数学专业的学生读。如果工科应用型学生，建议读华章数学的偏微分方程教程
很基础，很必要
专业性较强!
有点点难哦！但书不错哦1
Fritz.John本科用过的，极其让人难忘的书籍。写法比较几何化，此书并没有大量使用Sobolev空间的知识，适合看完一般数学物理方程之后再来看。也可以作为学习的参考。
Fritz John ,公认的大师级人物，内容由浅入深，但总起来说，还是有一些难度。难度主要来自John的语言，这本书的语言比一般数学书的弱智式英文曲折一点；其次是John写的比较简洁，要到达同样的结论，你常常会发现你走了和他完全不一样的思路——而且很可能是你错了。看得出John已经试图把这本书写的平民了，书里配了整整25幅图呢！尤其，这是PDE教材呢！最后，印刷清晰，比原版便宜多了。感谢影音图书出版业，啧。
写得非常简洁，但很深入，对每个专题都是很多的概念细节的阐释，而不是通篇的公式计算，所以读者自己需要做进一步的计算，涵盖了本科的内容，但是再次程度上不断延伸，很自然地引入了更深的东西，希望读这本书的同学不仅仅读懂lecture，不要只读上一遍，尽量反复看，领会作者处理pde的与其他分析手法不同的思路。还有，一定要做课后题，读数学书一定要做他的课后题，这本书 的课后题不都是那么简单，但是做出来之后能让你真正领会作者前面所讲内容的实质，对以后自己做研究有好处，做了题才能真正理解了fritz john。
很适合在有一定基础的情况下继续学习
以前的书都不错，就这次看着像盗版，有些失望
亚马逊的书最实惠服务也非常好。希望书之外的商品再多些！
最好能进到evans 的偏微分方程，这本书可以作为入门教材。
短小精悍，给人很精练的感觉，个人认为作为入门级教材还是可以的，深入学习的话可能有些浅了。